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In mathematics and physics, an equipotential or isopotential refers to a region in space where every point is at the same potential. [ 1 ] [ 2 ] [ 3 ] This usually refers to a scalar potential (in that case it is a level set of the potential), although it can also be applied to vector potentials .
The above equation describes the Earth's gravitational potential, not the geoid itself, at location ,,, the co-ordinate being the geocentric radius, i.e., distance from the Earth's centre. The geoid is a particular equipotential surface, [ 27 ] and is somewhat involved to compute.
Given the electrical potential on a conductor surface S i (the equipotential surface or the point P chosen on surface i) ... the system of linear equations is
The surfaces of constant geopotential or isosurfaces of the geopotential are called equigeopotential surfaces (sometimes abbreviated as geop), [1] also known as geopotential level surfaces, equipotential surfaces, or simply level surfaces. [2] Global mean sea surface is close to one equigeopotential called the geoid. [3]
Each ellipse or hyperbola in the pencil is the locus of points satisfying the equation ... In physics confocal ellipsoids appear as equipotential surfaces of a ...
This equation is valid provided ... Lines of constant ψ are known as streamlines and lines of constant φ are known as equipotential lines (see equipotential surface).
The electric field is perpendicular, locally, to the equipotential surface of the conductor, and zero inside; its flux πa 2 ·E, by Gauss's law equals πa 2 ·σ/ε 0. Thus, σ = ε 0 E . In problems involving conductors set at known potentials, the potential away from them is obtained by solving Laplace's equation , either analytically or ...
The geoid, or mathematical mean sea surface, is defined not only on the seas, but also under land; it is the equilibrium water surface that would result, would sea water be allowed to move freely (e.g., through tunnels) under the land. Technically, an equipotential surface of the true geopotential, chosen to coincide (on average) with mean sea ...